Sensitive thermal detectors should be useful for measuring very small energy pulses, such as those produced by the absorption of X-ray photons. The measurement uncertainty can be very small, making the technique promising for high resolution nondispersive X-ray spectroscopy. The limits to the energy resolution of such thermal detectors are derived and used to find the resolution to be expected for a detector suitable for X-ray spectroscopy in the 100 eV to 10,000 eV range. If there is no noise in the thermalization of the X-ray, resolution better than 1 eV full width at half maximum is possible for detectors operating at 0.1 K. Energy loss in the conversion of the photon energy to heat is a potential problem. The loss mechanisms may include emission of photons or electrons, or the trapping of energy in long lived metastable states. Fluctuations in the phonon spectrum could also limit the resolution if phonon relaxation times are very long. Conceptual solutions are given for each of these possible problems.